TUTM. Undergraduate Texts in Mathematics. Klaus Jänich. This is an intellectually stimulating, informal presentation of those parts of point set topology that are. Topology by Klaus Janich: Forward. Content. Sample. Back cover. Review. This is an intellectually stimulating, informal presentation of those parts of point set topology that are of importance to the nonspecialist.
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One point is that the argument mixedmath is giving is something that is directly verifiable at the point-set level. At the end of chapter three, which deals with the quotient topology, the author writes the following paragraph: Write a customer review.
The text is useful to all students of mathematics and physics alike. But since algebraic topology is so closely related to classical geometry, completely abstract reasoning would probably strip away much understanding of the sources of most of the central concepts,which I believe was Hatcher’s reason for writing the text in this manner.
The level of rigor that is needed depends on your own taste.
There’s a problem loading this menu right now. Please try again later. Post as a guest Name. I am taking a course in Algebraic Topology. Another example is the proof? It is not too often that a book about topology is written with the goal of actually explaining in detail what is going on behind the formalism.
Undergraduate Texts in Mathematics Hardcover: Janich, Topology ,page 49,translation by Silvio Levy It was later said by Levy that Janich told him that this particular passage was inspired by Janich’s concerns that German mathematical academia and textbooks in particular were beginning to become far too axiomatic and anti-visual and that this was hurting the clarity of presentations to students. Share your thoughts with other customers.
Just for the sections on Urysohn’s Lemma, Tietze’s Extension, and Tychonoff’s Theorem alone this book is worth owning – it contains the nicest proofs of these theorems I have ever seen. Does that make sense? In fact, here is direct quote from the index: Amazon Restaurants Food delivery from local restaurants. Would you like to tell us about a lower price? As for the larger question of how much rigor is necessary, I think a proof should contain enough rigor to provide a high-level sketch of how one would create a mechanically checkable proof, given enough time and energy.
Topology : K Janich :
Unless you are taking something on faith on purpose, but I get the feeling that is not your intent here, but rather you want to understand the material. Ships from and sold by Amazon. The German mathematician Klaus Janich has a wonderful response to this question in his book on topology, which is intentionally very non-rigorous and intuitive: Looking back, I was never uncomfortable with the kind of justifications we used to give in high school calculus and this current discomfiture stems from the fact that I have taken a few courses in Analysis in between.
toppology This is the most pleasurable text on general topology you are likely to find. Or, closer to topology, Toppology could say that collapsing the boundary of a closed disk to a point ‘clearly’ makes a sphere.
I almost always just tune out when people offer me their intuitions, and develop my own, for this reason. Quotient spaces,homotopy, complexes and urysohn and tietze lemma along with partitions of unity are tackled next. Counterexamples in Topology;Dover Books on Mathematics.
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Topology : Undergraduate Texts in Mathematics
The down side of this approach is that it completely disconnects the subject from it’s geometric roots and it becomes simply another branch of algebra whose roots are utterly mysterious.
The German mathematician Klaus Janich has a wonderful response to this question in his book on topology, which is intentionally very non-rigorous and intuitive:.
This is due to both a frequent lack of precision or formality in proofs and definitions coupled with a tendency to discuss much more ttopology material with which a student at this level wouldn’t be familiar. Shopbop Designer Fashion Brands. The author has a knack for allowing readers to “see into the future” of what kind of mathematics is waiting for them and how topology is indispensable in its study.
Physicists in particular, who must assimilate mathematics very quickly in order to apply it to real problems must have a pictorial, “playful” understanding of the mathematical constructions. Often algebraic topology texts assume that the reader is well acquainted with arguments of a previous course in point-set topology like this in order not to tooology trapped on details.
Second Edition Dover Books on Mathematics. Is this level of rigour acceptable? East Dane Designer Men’s Fashion.
Third Ajnich Dover Books on Mathematics. Concepts are often used before they are defined, or are not defined precisely, which is liable to frustrate these students as well. I have no doubt it will continue to undergo scrutiny in future ages.